Analysis of Unitarity in Conformal Quantum Gravity

Abstract

We perform a canonical quantization of Weyl's conformal gravity by means of the covariant operator formalism and investigate the unitarity of the resulting quantum theory. After reducing the originally fourth order theory to second order in time derivatives via the introduction of an auxiliary tensor field, we identify the full Fock space of quantum states under a BRST construction that includes Faddeev-Popov ghost fields corresponding to Weyl transformations. Using the Kugo-Ojima quartet mechanism, we identify the physical subspace of quantum states and find that the subspace containing the transverse spin-2 states comes equipped with an indefinite inner product metric and a one-particle Hamiltonian that possesses only a single eigenstate. We construct the LSZ reduction formula for the S-matrix in this spin-2 subspace and find that unitarity is violated in scattering events. The explicit way in which this violation occurs represents a new view on the ghost-problem in quadratic theories of quantum gravity.

v2: 31+11 pages, discussion changed and references added

References in corpus (5)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• The Ostrogradsky instability can be overcome by quantum physics
• Covariant BRST Quantization of Unimodular Gravity I -- Formulation with antisymmetric tensor ghosts --

Cited by in corpus (4)

• Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• High-energy properties of the graviton scattering in quadratic gravity
• Primordial Gravitational Waves in Quadratic Gravity